On Tue, 20 Jul 2004 20:58:22 -0700, Richard Hake wrote: [snip]
>Consider this: I was taught the multiplication tables in a rote way >many years ago. The tables were given to us on a piece of >cardboard, and we memorized each table and recited them in front of >the teacher. My children, by contrast, studied the concept of >multiplication by working on a chain of beads. Both they and I >could write down the answer "49" on a paper-and-pencil test that >asked "7 x 7= ?" But our actual knowing - both the process and the >extent - was quite different.
If you have the chance, would you please ask Martin Bickman to explain in detail how "our actual knowing - both the process and the extent - was quite different"?